Introduction

This guide covers the Missing Numbers topic for Constable GD aspirants. Master the concept, understand the tricks, and then test yourself with 10 practice MCQs.

Missing Numbers in Series — Concept Guide

Missing number problems test your ability to find the pattern in a sequence of numbers and identify the missing term. Patterns can be arithmetic, geometric, or based on special sequences.

Common Types

  • Arithmetic progression: Common difference (e.g., 2,5,8,11... +3)
  • Geometric progression: Common ratio (e.g., 3,9,27... ×3)
  • Square/Cube series: 1,4,9,16... or 1,8,27,64...
  • Fibonacci-type: Each term = sum of previous two
  • Difference series: Differences themselves form a pattern
  • Mixed operations: Alternating multiply/divide or add/subtract

⚡ Shortcuts & Tricks

  • Always find the difference between consecutive terms first.
  • If first differences are constant → arithmetic progression.
  • If ratios are constant → geometric progression.
  • If second differences are constant → the series is based on squares (quadratic).
  • Check if terms are perfect squares (1,4,9,16..) or cubes (1,8,27..).
  • Memorise squares up to 30 and cubes up to 15 for speed.

Practice MCQs — Missing Numbers (10 Questions)

Now test your understanding with these 10 questions:

Q1. 2, 4, 8, 16, __?

  • A. 32
  • B. 28
  • C. 24
  • D. 64
Answer: A — Each term doubles. 16×2=32.

Q2. 1, 4, 9, 16, 25, __?

  • A. 36
  • B. 49
  • C. 30
  • D. 32
Answer: A — Perfect squares: 1,4,9,16,25,36.

Q3. 3, 6, 11, 18, 27, __?

  • A. 38
  • B. 36
  • C. 40
  • D. 42
Answer: A — Differences: 3,5,7,9,11. Next: 27+11=38.

Q4. 1, 3, 7, 13, 21, __?

  • A. 31
  • B. 29
  • C. 33
  • D. 27
Answer: A — Differences: 2,4,6,8,10. Next: 21+10=31.

Q5. 2, 6, 12, 20, 30, __?

  • A. 42
  • B. 40
  • C. 44
  • D. 36
Answer: A — Differences: 4,6,8,10,12. Next: 30+12=42.

Q6. 5, 10, 20, 40, __?

  • A. 80
  • B. 60
  • C. 100
  • D. 70
Answer: A — Multiply by 2 each time. 40×2=80.

Q7. 100, 95, 85, 70, __?

  • A. 50
  • B. 55
  • C. 65
  • D. 45
Answer: A — Differences: 5,10,15,20. Next: 70-20=50.

Q8. 0, 1, 1, 2, 3, 5, 8, __?

  • A. 13
  • B. 10
  • C. 11
  • D. 12
Answer: A — Fibonacci: each term = sum of previous two. 5+8=13.

Q9. 7, 14, 28, 56, __?

  • A. 112
  • B. 100
  • C. 84
  • D. 96
Answer: A — Doubling series. 56×2=112.

Q10. 144, 121, 100, 81, __?

  • A. 64
  • B. 72
  • C. 49
  • D. 60
Answer: A — Perfect squares decreasing: 12²,11²,10²,9²,8²=64.

Summary

Missing Numbers is a scoring topic in Constable GD if you practise consistently. Focus on understanding the concept, apply the shortcut tricks, and practice regularly. Aim for 100% accuracy in this topic through regular revision.